1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 465,406 x 11
##    site_type date       sex    age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr>  <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 female miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 female miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 female 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 female 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 female 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 female 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 female 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 female 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 female 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 female 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 465,396 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##      date_report               nhs_region deaths
## 1     2020-03-01          East of England      0
## 2     2020-03-02          East of England      1
## 3     2020-03-03          East of England      0
## 4     2020-03-04          East of England      0
## 5     2020-03-05          East of England      0
## 6     2020-03-06          East of England      1
## 7     2020-03-07          East of England      0
## 8     2020-03-08          East of England      0
## 9     2020-03-09          East of England      1
## 10    2020-03-10          East of England      0
## 11    2020-03-11          East of England      0
## 12    2020-03-12          East of England      0
## 13    2020-03-13          East of England      1
## 14    2020-03-14          East of England      2
## 15    2020-03-15          East of England      2
## 16    2020-03-16          East of England      1
## 17    2020-03-17          East of England      1
## 18    2020-03-18          East of England      5
## 19    2020-03-19          East of England      4
## 20    2020-03-20          East of England      2
## 21    2020-03-21          East of England     11
## 22    2020-03-22          East of England     12
## 23    2020-03-23          East of England     11
## 24    2020-03-24          East of England     19
## 25    2020-03-25          East of England     26
## 26    2020-03-26          East of England     36
## 27    2020-03-27          East of England     38
## 28    2020-03-28          East of England     28
## 29    2020-03-29          East of England     43
## 30    2020-03-30          East of England     45
## 31    2020-03-31          East of England     70
## 32    2020-04-01          East of England     63
## 33    2020-04-02          East of England     65
## 34    2020-04-03          East of England     80
## 35    2020-04-04          East of England     71
## 36    2020-04-05          East of England     76
## 37    2020-04-06          East of England     71
## 38    2020-04-07          East of England     93
## 39    2020-04-08          East of England    111
## 40    2020-04-09          East of England     87
## 41    2020-04-10          East of England     74
## 42    2020-04-11          East of England     92
## 43    2020-04-12          East of England    100
## 44    2020-04-13          East of England     78
## 45    2020-04-14          East of England     61
## 46    2020-04-15          East of England     82
## 47    2020-04-16          East of England     74
## 48    2020-04-17          East of England     86
## 49    2020-04-18          East of England     64
## 50    2020-04-19          East of England     67
## 51    2020-04-20          East of England     67
## 52    2020-04-21          East of England     75
## 53    2020-04-22          East of England     67
## 54    2020-04-23          East of England     49
## 55    2020-04-24          East of England     66
## 56    2020-04-25          East of England     54
## 57    2020-04-26          East of England     48
## 58    2020-04-27          East of England     46
## 59    2020-04-28          East of England     58
## 60    2020-04-29          East of England     32
## 61    2020-04-30          East of England     45
## 62    2020-05-01          East of England     49
## 63    2020-05-02          East of England     29
## 64    2020-05-03          East of England     41
## 65    2020-05-04          East of England     19
## 66    2020-05-05          East of England     36
## 67    2020-05-06          East of England     31
## 68    2020-05-07          East of England     33
## 69    2020-05-08          East of England     33
## 70    2020-05-09          East of England     29
## 71    2020-05-10          East of England     22
## 72    2020-05-11          East of England     18
## 73    2020-05-12          East of England     21
## 74    2020-05-13          East of England     27
## 75    2020-05-14          East of England     26
## 76    2020-05-15          East of England     19
## 77    2020-05-16          East of England     26
## 78    2020-05-17          East of England     17
## 79    2020-05-18          East of England     25
## 80    2020-05-19          East of England     15
## 81    2020-05-20          East of England     26
## 82    2020-05-21          East of England     21
## 83    2020-05-22          East of England     13
## 84    2020-05-23          East of England     12
## 85    2020-05-24          East of England     17
## 86    2020-05-25          East of England     25
## 87    2020-05-26          East of England     14
## 88    2020-05-27          East of England     12
## 89    2020-05-28          East of England     17
## 90    2020-05-29          East of England     16
## 91    2020-05-30          East of England      9
## 92    2020-05-31          East of England      8
## 93    2020-06-01          East of England     17
## 94    2020-06-02          East of England     14
## 95    2020-06-03          East of England     10
## 96    2020-06-04          East of England      7
## 97    2020-06-05          East of England     14
## 98    2020-06-06          East of England      5
## 99    2020-06-07          East of England      9
## 100   2020-06-08          East of England      7
## 101   2020-06-09          East of England      6
## 102   2020-06-10          East of England      8
## 103   2020-06-11          East of England      1
## 104   2020-06-12          East of England      9
## 105   2020-06-13          East of England      5
## 106   2020-06-14          East of England      4
## 107   2020-06-15          East of England      8
## 108   2020-06-16          East of England      3
## 109   2020-06-17          East of England      7
## 110   2020-06-18          East of England      4
## 111   2020-06-19          East of England      7
## 112   2020-06-20          East of England      4
## 113   2020-06-21          East of England      3
## 114   2020-06-22          East of England      6
## 115   2020-06-23          East of England      5
## 116   2020-06-24          East of England      4
## 117   2020-06-25          East of England      1
## 118   2020-06-26          East of England      6
## 119   2020-06-27          East of England      6
## 120   2020-06-28          East of England      8
## 121   2020-06-29          East of England      4
## 122   2020-06-30          East of England      5
## 123   2020-07-01          East of England      2
## 124   2020-07-02          East of England      5
## 125   2020-07-03          East of England      0
## 126   2020-07-04          East of England      3
## 127   2020-07-05          East of England      1
## 128   2020-07-06          East of England      2
## 129   2020-07-07          East of England      2
## 130   2020-07-08          East of England      0
## 131   2020-07-09          East of England      8
## 132   2020-07-10          East of England      4
## 133   2020-07-11          East of England      2
## 134   2020-07-12          East of England      1
## 135   2020-07-13          East of England      8
## 136   2020-07-14          East of England      2
## 137   2020-07-15          East of England      0
## 138   2020-07-16          East of England      0
## 139   2020-07-17          East of England      0
## 140   2020-07-18          East of England      0
## 141   2020-07-19          East of England      1
## 142   2020-07-20          East of England      1
## 143   2020-07-21          East of England      1
## 144   2020-07-22          East of England      2
## 145   2020-07-23          East of England      1
## 146   2020-07-24          East of England      1
## 147   2020-07-25          East of England      0
## 148   2020-07-26          East of England      1
## 149   2020-07-27          East of England      1
## 150   2020-07-28          East of England      2
## 151   2020-07-29          East of England      0
## 152   2020-07-30          East of England      0
## 153   2020-07-31          East of England      1
## 154   2020-08-01          East of England      0
## 155   2020-08-02          East of England      0
## 156   2020-08-03          East of England      0
## 157   2020-08-04          East of England      1
## 158   2020-08-05          East of England      1
## 159   2020-08-06          East of England      0
## 160   2020-08-07          East of England      1
## 161   2020-08-08          East of England      0
## 162   2020-08-09          East of England      0
## 163   2020-08-10          East of England      1
## 164   2020-08-11          East of England      2
## 165   2020-08-12          East of England      1
## 166   2020-08-13          East of England      0
## 167   2020-08-14          East of England      1
## 168   2020-08-15          East of England      1
## 169   2020-08-16          East of England      0
## 170   2020-08-17          East of England      0
## 171   2020-08-18          East of England      2
## 172   2020-08-19          East of England      1
## 173   2020-08-20          East of England      1
## 174   2020-08-21          East of England      0
## 175   2020-08-22          East of England      1
## 176   2020-08-23          East of England      1
## 177   2020-08-24          East of England      0
## 178   2020-08-25          East of England      0
## 179   2020-08-26          East of England      1
## 180   2020-08-27          East of England      1
## 181   2020-08-28          East of England      0
## 182   2020-08-29          East of England      0
## 183   2020-08-30          East of England      0
## 184   2020-08-31          East of England      0
## 185   2020-09-01          East of England      0
## 186   2020-09-02          East of England      0
## 187   2020-09-03          East of England      1
## 188   2020-09-04          East of England      1
## 189   2020-09-05          East of England      0
## 190   2020-09-06          East of England      1
## 191   2020-09-07          East of England      0
## 192   2020-09-08          East of England      0
## 193   2020-09-09          East of England      0
## 194   2020-09-10          East of England      0
## 195   2020-09-11          East of England      0
## 196   2020-09-12          East of England      0
## 197   2020-09-13          East of England      1
## 198   2020-09-14          East of England      1
## 199   2020-09-15          East of England      0
## 200   2020-09-16          East of England      0
## 201   2020-09-17          East of England      0
## 202   2020-09-18          East of England      0
## 203   2020-09-19          East of England      0
## 204   2020-09-20          East of England      2
## 205   2020-09-21          East of England      0
## 206   2020-09-22          East of England      2
## 207   2020-09-23          East of England      1
## 208   2020-09-24          East of England      0
## 209   2020-09-25          East of England      1
## 210   2020-09-26          East of England      1
## 211   2020-09-27          East of England      1
## 212   2020-09-28          East of England      2
## 213   2020-09-29          East of England      2
## 214   2020-09-30          East of England      2
## 215   2020-10-01          East of England      2
## 216   2020-10-02          East of England      1
## 217   2020-10-03          East of England      1
## 218   2020-10-04          East of England      0
## 219   2020-10-05          East of England      0
## 220   2020-10-06          East of England      4
## 221   2020-10-07          East of England      6
## 222   2020-10-08          East of England      3
## 223   2020-10-09          East of England      1
## 224   2020-10-10          East of England      6
## 225   2020-10-11          East of England      2
## 226   2020-10-12          East of England      2
## 227   2020-10-13          East of England      1
## 228   2020-10-14          East of England      3
## 229   2020-10-15          East of England      4
## 230   2020-10-16          East of England      5
## 231   2020-10-17          East of England      6
## 232   2020-10-18          East of England      7
## 233   2020-10-19          East of England      5
## 234   2020-10-20          East of England      9
## 235   2020-10-21          East of England      8
## 236   2020-10-22          East of England      7
## 237   2020-10-23          East of England     14
## 238   2020-10-24          East of England      1
## 239   2020-10-25          East of England     10
## 240   2020-10-26          East of England     10
## 241   2020-10-27          East of England      8
## 242   2020-10-28          East of England     12
## 243   2020-10-29          East of England     10
## 244   2020-10-30          East of England     12
## 245   2020-10-31          East of England     15
## 246   2020-11-01          East of England     14
## 247   2020-11-02          East of England      9
## 248   2020-11-03          East of England     14
## 249   2020-11-04          East of England     11
## 250   2020-11-05          East of England     12
## 251   2020-11-06          East of England     19
## 252   2020-11-07          East of England     10
## 253   2020-11-08          East of England     13
## 254   2020-11-09          East of England     16
## 255   2020-11-10          East of England     26
## 256   2020-11-11          East of England     14
## 257   2020-11-12          East of England     14
## 258   2020-11-13          East of England     21
## 259   2020-11-14          East of England     19
## 260   2020-11-15          East of England     13
## 261   2020-11-16          East of England     11
## 262   2020-11-17          East of England     17
## 263   2020-11-18          East of England     19
## 264   2020-11-19          East of England     23
## 265   2020-11-20          East of England     24
## 266   2020-11-21          East of England     19
## 267   2020-11-22          East of England     21
## 268   2020-11-23          East of England     18
## 269   2020-11-24          East of England     21
## 270   2020-11-25          East of England     19
## 271   2020-11-26          East of England     19
## 272   2020-11-27          East of England     14
## 273   2020-11-28          East of England     28
## 274   2020-11-29          East of England     19
## 275   2020-11-30          East of England     22
## 276   2020-12-01          East of England     26
## 277   2020-12-02          East of England     18
## 278   2020-12-03          East of England     24
## 279   2020-12-04          East of England     25
## 280   2020-12-05          East of England     25
## 281   2020-12-06          East of England     22
## 282   2020-12-07          East of England     16
## 283   2020-12-08          East of England     26
## 284   2020-12-09          East of England     20
## 285   2020-12-10          East of England     32
## 286   2020-12-11          East of England     32
## 287   2020-12-12          East of England     27
## 288   2020-12-13          East of England     25
## 289   2020-12-14          East of England     32
## 290   2020-12-15          East of England     35
## 291   2020-12-16          East of England     29
## 292   2020-12-17          East of England     43
## 293   2020-12-18          East of England     44
## 294   2020-12-19          East of England     54
## 295   2020-12-20          East of England     52
## 296   2020-12-21          East of England     66
## 297   2020-12-22          East of England     52
## 298   2020-12-23          East of England     62
## 299   2020-12-24          East of England     61
## 300   2020-12-25          East of England     58
## 301   2020-12-26          East of England     64
## 302   2020-12-27          East of England     54
## 303   2020-12-28          East of England     71
## 304   2020-12-29          East of England     54
## 305   2020-12-30          East of England     76
## 306   2020-12-31          East of England     82
## 307   2021-01-01          East of England     90
## 308   2021-01-02          East of England     66
## 309   2021-01-03          East of England     78
## 310   2021-01-04          East of England     88
## 311   2021-01-05          East of England    102
## 312   2021-01-06          East of England    100
## 313   2021-01-07          East of England    116
## 314   2021-01-08          East of England     97
## 315   2021-01-09          East of England    133
## 316   2021-01-10          East of England    125
## 317   2021-01-11          East of England    126
## 318   2021-01-12          East of England    131
## 319   2021-01-13          East of England    131
## 320   2021-01-14          East of England    128
## 321   2021-01-15          East of England    119
## 322   2021-01-16          East of England    132
## 323   2021-01-17          East of England    133
## 324   2021-01-18          East of England    120
## 325   2021-01-19          East of England    130
## 326   2021-01-20          East of England    147
## 327   2021-01-21          East of England    135
## 328   2021-01-22          East of England    123
## 329   2021-01-23          East of England    102
## 330   2021-01-24          East of England    101
## 331   2021-01-25          East of England    114
## 332   2021-01-26          East of England     89
## 333   2021-01-27          East of England     94
## 334   2021-01-28          East of England    110
## 335   2021-01-29          East of England     96
## 336   2021-01-30          East of England     85
## 337   2021-01-31          East of England     74
## 338   2021-02-01          East of England     67
## 339   2021-02-02          East of England     74
## 340   2021-02-03          East of England     82
## 341   2021-02-04          East of England     75
## 342   2021-02-05          East of England     66
## 343   2021-02-06          East of England     78
## 344   2021-02-07          East of England     62
## 345   2021-02-08          East of England     73
## 346   2021-02-09          East of England     63
## 347   2021-02-10          East of England     53
## 348   2021-02-11          East of England     52
## 349   2021-02-12          East of England     47
## 350   2021-02-13          East of England     47
## 351   2021-02-14          East of England     33
## 352   2021-02-15          East of England     48
## 353   2021-02-16          East of England     47
## 354   2021-02-17          East of England     46
## 355   2021-02-18          East of England     31
## 356   2021-02-19          East of England     28
## 357   2021-02-20          East of England     30
## 358   2021-02-21          East of England     24
## 359   2021-02-22          East of England     26
## 360   2021-02-23          East of England     28
## 361   2021-02-24          East of England     17
## 362   2021-02-25          East of England     23
## 363   2021-02-26          East of England     15
## 364   2021-02-27          East of England     23
## 365   2021-02-28          East of England     17
## 366   2021-03-01          East of England     18
## 367   2021-03-02          East of England     19
## 368   2021-03-03          East of England     12
## 369   2021-03-04          East of England     18
## 370   2021-03-05          East of England     12
## 371   2021-03-06          East of England     12
## 372   2021-03-07          East of England     14
## 373   2021-03-08          East of England     15
## 374   2021-03-09          East of England     11
## 375   2021-03-10          East of England      7
## 376   2021-03-11          East of England     11
## 377   2021-03-12          East of England      2
## 378   2021-03-13          East of England      1
## 379   2020-03-01                   London      0
## 380   2020-03-02                   London      0
## 381   2020-03-03                   London      0
## 382   2020-03-04                   London      0
## 383   2020-03-05                   London      0
## 384   2020-03-06                   London      1
## 385   2020-03-07                   London      0
## 386   2020-03-08                   London      0
## 387   2020-03-09                   London      1
## 388   2020-03-10                   London      0
## 389   2020-03-11                   London      5
## 390   2020-03-12                   London      6
## 391   2020-03-13                   London     10
## 392   2020-03-14                   London     13
## 393   2020-03-15                   London      9
## 394   2020-03-16                   London     15
## 395   2020-03-17                   London     23
## 396   2020-03-18                   London     28
## 397   2020-03-19                   London     25
## 398   2020-03-20                   London     44
## 399   2020-03-21                   London     49
## 400   2020-03-22                   London     54
## 401   2020-03-23                   London     63
## 402   2020-03-24                   London     86
## 403   2020-03-25                   London    112
## 404   2020-03-26                   London    130
## 405   2020-03-27                   London    130
## 406   2020-03-28                   London    123
## 407   2020-03-29                   London    145
## 408   2020-03-30                   London    151
## 409   2020-03-31                   London    183
## 410   2020-04-01                   London    202
## 411   2020-04-02                   London    191
## 412   2020-04-03                   London    199
## 413   2020-04-04                   London    231
## 414   2020-04-05                   London    195
## 415   2020-04-06                   London    198
## 416   2020-04-07                   London    220
## 417   2020-04-08                   London    239
## 418   2020-04-09                   London    207
## 419   2020-04-10                   London    171
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## 1448  2021-01-08 North East and Yorkshire     67
## 1449  2021-01-09 North East and Yorkshire     58
## 1450  2021-01-10 North East and Yorkshire     80
## 1451  2021-01-11 North East and Yorkshire     82
## 1452  2021-01-12 North East and Yorkshire     69
## 1453  2021-01-13 North East and Yorkshire     77
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## 1462  2021-01-22 North East and Yorkshire     80
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## 1471  2021-01-31 North East and Yorkshire     81
## 1472  2021-02-01 North East and Yorkshire     79
## 1473  2021-02-02 North East and Yorkshire     69
## 1474  2021-02-03 North East and Yorkshire     81
## 1475  2021-02-04 North East and Yorkshire     68
## 1476  2021-02-05 North East and Yorkshire     80
## 1477  2021-02-06 North East and Yorkshire     52
## 1478  2021-02-07 North East and Yorkshire     59
## 1479  2021-02-08 North East and Yorkshire     51
## 1480  2021-02-09 North East and Yorkshire     53
## 1481  2021-02-10 North East and Yorkshire     62
## 1482  2021-02-11 North East and Yorkshire     64
## 1483  2021-02-12 North East and Yorkshire     59
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## 1485  2021-02-14 North East and Yorkshire     59
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## 1487  2021-02-16 North East and Yorkshire     46
## 1488  2021-02-17 North East and Yorkshire     48
## 1489  2021-02-18 North East and Yorkshire     44
## 1490  2021-02-19 North East and Yorkshire     42
## 1491  2021-02-20 North East and Yorkshire     37
## 1492  2021-02-21 North East and Yorkshire     39
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## 1502  2021-03-03 North East and Yorkshire     27
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## 1514  2020-03-02               North West      0
## 1515  2020-03-03               North West      0
## 1516  2020-03-04               North West      0
## 1517  2020-03-05               North West      1
## 1518  2020-03-06               North West      0
## 1519  2020-03-07               North West      0
## 1520  2020-03-08               North West      1
## 1521  2020-03-09               North West      0
## 1522  2020-03-10               North West      0
## 1523  2020-03-11               North West      0
## 1524  2020-03-12               North West      2
## 1525  2020-03-13               North West      3
## 1526  2020-03-14               North West      1
## 1527  2020-03-15               North West      4
## 1528  2020-03-16               North West      2
## 1529  2020-03-17               North West      4
## 1530  2020-03-18               North West      6
## 1531  2020-03-19               North West      7
## 1532  2020-03-20               North West     10
## 1533  2020-03-21               North West     11
## 1534  2020-03-22               North West     13
## 1535  2020-03-23               North West     15
## 1536  2020-03-24               North West     21
## 1537  2020-03-25               North West     21
## 1538  2020-03-26               North West     29
## 1539  2020-03-27               North West     36
## 1540  2020-03-28               North West     28
## 1541  2020-03-29               North West     46
## 1542  2020-03-30               North West     67
## 1543  2020-03-31               North West     52
## 1544  2020-04-01               North West     86
## 1545  2020-04-02               North West     96
## 1546  2020-04-03               North West     95
## 1547  2020-04-04               North West     98
## 1548  2020-04-05               North West    102
## 1549  2020-04-06               North West    100
## 1550  2020-04-07               North West    136
## 1551  2020-04-08               North West    127
## 1552  2020-04-09               North West    119
## 1553  2020-04-10               North West    117
## 1554  2020-04-11               North West    138
## 1555  2020-04-12               North West    125
## 1556  2020-04-13               North West    130
## 1557  2020-04-14               North West    130
## 1558  2020-04-15               North West    114
## 1559  2020-04-16               North West    135
## 1560  2020-04-17               North West     98
## 1561  2020-04-18               North West    114
## 1562  2020-04-19               North West     71
## 1563  2020-04-20               North West     83
## 1564  2020-04-21               North West     76
## 1565  2020-04-22               North West     87
## 1566  2020-04-23               North West     85
## 1567  2020-04-24               North West     67
## 1568  2020-04-25               North West     67
## 1569  2020-04-26               North West     55
## 1570  2020-04-27               North West     54
## 1571  2020-04-28               North West     57
## 1572  2020-04-29               North West     64
## 1573  2020-04-30               North West     60
## 1574  2020-05-01               North West     45
## 1575  2020-05-02               North West     56
## 1576  2020-05-03               North West     55
## 1577  2020-05-04               North West     48
## 1578  2020-05-05               North West     49
## 1579  2020-05-06               North West     44
## 1580  2020-05-07               North West     50
## 1581  2020-05-08               North West     43
## 1582  2020-05-09               North West     31
## 1583  2020-05-10               North West     42
## 1584  2020-05-11               North West     35
## 1585  2020-05-12               North West     38
## 1586  2020-05-13               North West     25
## 1587  2020-05-14               North West     26
## 1588  2020-05-15               North West     33
## 1589  2020-05-16               North West     32
## 1590  2020-05-17               North West     24
## 1591  2020-05-18               North West     31
## 1592  2020-05-19               North West     35
## 1593  2020-05-20               North West     27
## 1594  2020-05-21               North West     28
## 1595  2020-05-22               North West     26
## 1596  2020-05-23               North West     31
## 1597  2020-05-24               North West     26
## 1598  2020-05-25               North West     31
## 1599  2020-05-26               North West     27
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## 1601  2020-05-28               North West     28
## 1602  2020-05-29               North West     20
## 1603  2020-05-30               North West     19
## 1604  2020-05-31               North West     13
## 1605  2020-06-01               North West     12
## 1606  2020-06-02               North West     27
## 1607  2020-06-03               North West     22
## 1608  2020-06-04               North West     22
## 1609  2020-06-05               North West     16
## 1610  2020-06-06               North West     26
## 1611  2020-06-07               North West     20
## 1612  2020-06-08               North West     23
## 1613  2020-06-09               North West     17
## 1614  2020-06-10               North West     16
## 1615  2020-06-11               North West     16
## 1616  2020-06-12               North West     11
## 1617  2020-06-13               North West     10
## 1618  2020-06-14               North West     15
## 1619  2020-06-15               North West     16
## 1620  2020-06-16               North West     16
## 1621  2020-06-17               North West     13
## 1622  2020-06-18               North West     14
## 1623  2020-06-19               North West      7
## 1624  2020-06-20               North West     11
## 1625  2020-06-21               North West      8
## 1626  2020-06-22               North West     11
## 1627  2020-06-23               North West     13
## 1628  2020-06-24               North West     13
## 1629  2020-06-25               North West     15
## 1630  2020-06-26               North West      6
## 1631  2020-06-27               North West      7
## 1632  2020-06-28               North West      9
## 1633  2020-06-29               North West      9
## 1634  2020-06-30               North West      7
## 1635  2020-07-01               North West      3
## 1636  2020-07-02               North West      6
## 1637  2020-07-03               North West      7
## 1638  2020-07-04               North West      4
## 1639  2020-07-05               North West      6
## 1640  2020-07-06               North West      9
## 1641  2020-07-07               North West      8
## 1642  2020-07-08               North West      5
## 1643  2020-07-09               North West     10
## 1644  2020-07-10               North West      2
## 1645  2020-07-11               North West      5
## 1646  2020-07-12               North West      0
## 1647  2020-07-13               North West      6
## 1648  2020-07-14               North West      4
## 1649  2020-07-15               North West      5
## 1650  2020-07-16               North West      2
## 1651  2020-07-17               North West      4
## 1652  2020-07-18               North West      5
## 1653  2020-07-19               North West      3
## 1654  2020-07-20               North West      0
## 1655  2020-07-21               North West      2
## 1656  2020-07-22               North West      3
## 1657  2020-07-23               North West      3
## 1658  2020-07-24               North West      1
## 1659  2020-07-25               North West      1
## 1660  2020-07-26               North West      3
## 1661  2020-07-27               North West      1
## 1662  2020-07-28               North West      1
## 1663  2020-07-29               North West      2
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## 1665  2020-07-31               North West      0
## 1666  2020-08-01               North West      2
## 1667  2020-08-02               North West      1
## 1668  2020-08-03               North West      8
## 1669  2020-08-04               North West      3
## 1670  2020-08-05               North West      2
## 1671  2020-08-06               North West      2
## 1672  2020-08-07               North West      2
## 1673  2020-08-08               North West      2
## 1674  2020-08-09               North West      3
## 1675  2020-08-10               North West      2
## 1676  2020-08-11               North West      3
## 1677  2020-08-12               North West      0
## 1678  2020-08-13               North West      2
## 1679  2020-08-14               North West      2
## 1680  2020-08-15               North West      6
## 1681  2020-08-16               North West      2
## 1682  2020-08-17               North West      1
## 1683  2020-08-18               North West      2
## 1684  2020-08-19               North West      1
## 1685  2020-08-20               North West      1
## 1686  2020-08-21               North West      4
## 1687  2020-08-22               North West      3
## 1688  2020-08-23               North West      5
## 1689  2020-08-24               North West      4
## 1690  2020-08-25               North West      3
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## 1692  2020-08-27               North West      1
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## 1694  2020-08-29               North West      0
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## 1699  2020-09-03               North West      1
## 1700  2020-09-04               North West      3
## 1701  2020-09-05               North West      6
## 1702  2020-09-06               North West      1
## 1703  2020-09-07               North West      8
## 1704  2020-09-08               North West      6
## 1705  2020-09-09               North West      5
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## 1709  2020-09-13               North West      2
## 1710  2020-09-14               North West      4
## 1711  2020-09-15               North West      4
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## 1714  2020-09-18               North West      6
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## 1720  2020-09-24               North West     10
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## 1727  2020-10-01               North West     17
## 1728  2020-10-02               North West     20
## 1729  2020-10-03               North West     15
## 1730  2020-10-04               North West     15
## 1731  2020-10-05               North West     15
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## 1748  2020-10-22               North West     49
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## 1750  2020-10-24               North West     51
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## 1752  2020-10-26               North West     53
## 1753  2020-10-27               North West     49
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## 1755  2020-10-29               North West     74
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## 1757  2020-10-31               North West     63
## 1758  2020-11-01               North West     76
## 1759  2020-11-02               North West     65
## 1760  2020-11-03               North West     77
## 1761  2020-11-04               North West     64
## 1762  2020-11-05               North West     67
## 1763  2020-11-06               North West     76
## 1764  2020-11-07               North West     79
## 1765  2020-11-08               North West     83
## 1766  2020-11-09               North West     82
## 1767  2020-11-10               North West     68
## 1768  2020-11-11               North West     62
## 1769  2020-11-12               North West     64
## 1770  2020-11-13               North West     81
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## 1773  2020-11-16               North West     74
## 1774  2020-11-17               North West     73
## 1775  2020-11-18               North West     71
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## 1779  2020-11-22               North West     52
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## 1789  2020-12-02               North West     48
## 1790  2020-12-03               North West     47
## 1791  2020-12-04               North West     48
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## 1795  2020-12-08               North West     49
## 1796  2020-12-09               North West     48
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## 1822  2021-01-04               North West     51
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## 1849  2021-01-31               North West     85
## 1850  2021-02-01               North West     96
## 1851  2021-02-02               North West     82
## 1852  2021-02-03               North West     71
## 1853  2021-02-04               North West     79
## 1854  2021-02-05               North West     67
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## 1856  2021-02-07               North West     53
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## 1858  2021-02-09               North West     69
## 1859  2021-02-10               North West     72
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## 1863  2021-02-14               North West     50
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## 1866  2021-02-17               North West     55
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## 1868  2021-02-19               North West     40
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## 1872  2021-02-23               North West     35
## 1873  2021-02-24               North West     34
## 1874  2021-02-25               North West     22
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## 1879  2021-03-02               North West     13
## 1880  2021-03-03               North West     21
## 1881  2021-03-04               North West     12
## 1882  2021-03-05               North West     25
## 1883  2021-03-06               North West     14
## 1884  2021-03-07               North West     23
## 1885  2021-03-08               North West     16
## 1886  2021-03-09               North West     14
## 1887  2021-03-10               North West     11
## 1888  2021-03-11               North West     15
## 1889  2021-03-12               North West      4
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## 1893  2020-03-03               South East      1
## 1894  2020-03-04               South East      0
## 1895  2020-03-05               South East      1
## 1896  2020-03-06               South East      0
## 1897  2020-03-07               South East      0
## 1898  2020-03-08               South East      1
## 1899  2020-03-09               South East      1
## 1900  2020-03-10               South East      1
## 1901  2020-03-11               South East      1
## 1902  2020-03-12               South East      0
## 1903  2020-03-13               South East      1
## 1904  2020-03-14               South East      1
## 1905  2020-03-15               South East      5
## 1906  2020-03-16               South East      8
## 1907  2020-03-17               South East      7
## 1908  2020-03-18               South East     10
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## 1910  2020-03-20               South East     13
## 1911  2020-03-21               South East      7
## 1912  2020-03-22               South East     25
## 1913  2020-03-23               South East     20
## 1914  2020-03-24               South East     22
## 1915  2020-03-25               South East     29
## 1916  2020-03-26               South East     35
## 1917  2020-03-27               South East     36
## 1918  2020-03-28               South East     36
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## 1921  2020-03-31               South East     65
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## 1923  2020-04-02               South East     55
## 1924  2020-04-03               South East     72
## 1925  2020-04-04               South East     80
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## 1928  2020-04-07               South East    100
## 1929  2020-04-08               South East     83
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## 1936  2020-04-15               South East     72
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## 1939  2020-04-18               South East     57
## 1940  2020-04-19               South East     70
## 1941  2020-04-20               South East     87
## 1942  2020-04-21               South East     51
## 1943  2020-04-22               South East     54
## 1944  2020-04-23               South East     57
## 1945  2020-04-24               South East     64
## 1946  2020-04-25               South East     51
## 1947  2020-04-26               South East     51
## 1948  2020-04-27               South East     41
## 1949  2020-04-28               South East     40
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## 1951  2020-04-30               South East     29
## 1952  2020-05-01               South East     37
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## 2457  2020-09-05               South West      0
## 2458  2020-09-06               South West      0
## 2459  2020-09-07               South West      0
## 2460  2020-09-08               South West      1
## 2461  2020-09-09               South West      0
## 2462  2020-09-10               South West      0
## 2463  2020-09-11               South West      0
## 2464  2020-09-12               South West      0
## 2465  2020-09-13               South West      1
## 2466  2020-09-14               South West      0
## 2467  2020-09-15               South West      0
## 2468  2020-09-16               South West      0
## 2469  2020-09-17               South West      1
## 2470  2020-09-18               South West      0
## 2471  2020-09-19               South West      0
## 2472  2020-09-20               South West      1
## 2473  2020-09-21               South West      0
## 2474  2020-09-22               South West      0
## 2475  2020-09-23               South West      0
## 2476  2020-09-24               South West      1
## 2477  2020-09-25               South West      0
## 2478  2020-09-26               South West      0
## 2479  2020-09-27               South West      0
## 2480  2020-09-28               South West      0
## 2481  2020-09-29               South West      0
## 2482  2020-09-30               South West      0
## 2483  2020-10-01               South West      0
## 2484  2020-10-02               South West      1
## 2485  2020-10-03               South West      0
## 2486  2020-10-04               South West      0
## 2487  2020-10-05               South West      0
## 2488  2020-10-06               South West      1
## 2489  2020-10-07               South West      0
## 2490  2020-10-08               South West      1
## 2491  2020-10-09               South West      1
## 2492  2020-10-10               South West      0
## 2493  2020-10-11               South West      4
## 2494  2020-10-12               South West      2
## 2495  2020-10-13               South West      0
## 2496  2020-10-14               South West      3
## 2497  2020-10-15               South West      1
## 2498  2020-10-16               South West      2
## 2499  2020-10-17               South West      8
## 2500  2020-10-18               South West      2
## 2501  2020-10-19               South West      2
## 2502  2020-10-20               South West      3
## 2503  2020-10-21               South West      6
## 2504  2020-10-22               South West      6
## 2505  2020-10-23               South West      5
## 2506  2020-10-24               South West      5
## 2507  2020-10-25               South West      5
## 2508  2020-10-26               South West      7
## 2509  2020-10-27               South West      6
## 2510  2020-10-28               South West      8
## 2511  2020-10-29               South West     11
## 2512  2020-10-30               South West      8
## 2513  2020-10-31               South West      5
## 2514  2020-11-01               South West      5
## 2515  2020-11-02               South West     11
## 2516  2020-11-03               South West      7
## 2517  2020-11-04               South West      8
## 2518  2020-11-05               South West      5
## 2519  2020-11-06               South West     11
## 2520  2020-11-07               South West     10
## 2521  2020-11-08               South West     10
## 2522  2020-11-09               South West     12
## 2523  2020-11-10               South West      6
## 2524  2020-11-11               South West     13
## 2525  2020-11-12               South West     17
## 2526  2020-11-13               South West      9
## 2527  2020-11-14               South West      8
## 2528  2020-11-15               South West     16
## 2529  2020-11-16               South West     18
## 2530  2020-11-17               South West     17
## 2531  2020-11-18               South West     26
## 2532  2020-11-19               South West     15
## 2533  2020-11-20               South West     25
## 2534  2020-11-21               South West     25
## 2535  2020-11-22               South West     24
## 2536  2020-11-23               South West     14
## 2537  2020-11-24               South West     20
## 2538  2020-11-25               South West     25
## 2539  2020-11-26               South West     16
## 2540  2020-11-27               South West     21
## 2541  2020-11-28               South West     35
## 2542  2020-11-29               South West     15
## 2543  2020-11-30               South West     22
## 2544  2020-12-01               South West     19
## 2545  2020-12-02               South West     15
## 2546  2020-12-03               South West     14
## 2547  2020-12-04               South West     20
## 2548  2020-12-05               South West     17
## 2549  2020-12-06               South West     13
## 2550  2020-12-07               South West     16
## 2551  2020-12-08               South West     19
## 2552  2020-12-09               South West     22
## 2553  2020-12-10               South West     21
## 2554  2020-12-11               South West     20
## 2555  2020-12-12               South West     15
## 2556  2020-12-13               South West     19
## 2557  2020-12-14               South West     20
## 2558  2020-12-15               South West     20
## 2559  2020-12-16               South West      9
## 2560  2020-12-17               South West     26
## 2561  2020-12-18               South West     11
## 2562  2020-12-19               South West     22
## 2563  2020-12-20               South West     19
## 2564  2020-12-21               South West     22
## 2565  2020-12-22               South West     11
## 2566  2020-12-23               South West     16
## 2567  2020-12-24               South West     18
## 2568  2020-12-25               South West     19
## 2569  2020-12-26               South West     24
## 2570  2020-12-27               South West     24
## 2571  2020-12-28               South West     21
## 2572  2020-12-29               South West     20
## 2573  2020-12-30               South West     17
## 2574  2020-12-31               South West     28
## 2575  2021-01-01               South West     29
## 2576  2021-01-02               South West     24
## 2577  2021-01-03               South West     28
## 2578  2021-01-04               South West     33
## 2579  2021-01-05               South West     31
## 2580  2021-01-06               South West     27
## 2581  2021-01-07               South West     31
## 2582  2021-01-08               South West     34
## 2583  2021-01-09               South West     26
## 2584  2021-01-10               South West     34
## 2585  2021-01-11               South West     40
## 2586  2021-01-12               South West     53
## 2587  2021-01-13               South West     43
## 2588  2021-01-14               South West     39
## 2589  2021-01-15               South West     47
## 2590  2021-01-16               South West     57
## 2591  2021-01-17               South West     42
## 2592  2021-01-18               South West     47
## 2593  2021-01-19               South West     45
## 2594  2021-01-20               South West     65
## 2595  2021-01-21               South West     62
## 2596  2021-01-22               South West     60
## 2597  2021-01-23               South West     54
## 2598  2021-01-24               South West     59
## 2599  2021-01-25               South West     62
## 2600  2021-01-26               South West     47
## 2601  2021-01-27               South West     46
## 2602  2021-01-28               South West     52
## 2603  2021-01-29               South West     42
## 2604  2021-01-30               South West     39
## 2605  2021-01-31               South West     36
## 2606  2021-02-01               South West     29
## 2607  2021-02-02               South West     38
## 2608  2021-02-03               South West     32
## 2609  2021-02-04               South West     33
## 2610  2021-02-05               South West     25
## 2611  2021-02-06               South West     39
## 2612  2021-02-07               South West     35
## 2613  2021-02-08               South West     32
## 2614  2021-02-09               South West     31
## 2615  2021-02-10               South West     18
## 2616  2021-02-11               South West     19
## 2617  2021-02-12               South West     28
## 2618  2021-02-13               South West     29
## 2619  2021-02-14               South West     17
## 2620  2021-02-15               South West     22
## 2621  2021-02-16               South West     12
## 2622  2021-02-17               South West     20
## 2623  2021-02-18               South West     21
## 2624  2021-02-19               South West     18
## 2625  2021-02-20               South West     12
## 2626  2021-02-21               South West     16
## 2627  2021-02-22               South West     11
## 2628  2021-02-23               South West      6
## 2629  2021-02-24               South West      9
## 2630  2021-02-25               South West     12
## 2631  2021-02-26               South West      7
## 2632  2021-02-27               South West      6
## 2633  2021-02-28               South West     10
## 2634  2021-03-01               South West     15
## 2635  2021-03-02               South West      8
## 2636  2021-03-03               South West      3
## 2637  2021-03-04               South West      4
## 2638  2021-03-05               South West      4
## 2639  2021-03-06               South West      6
## 2640  2021-03-07               South West      1
## 2641  2021-03-08               South West      8
## 2642  2021-03-09               South West      3
## 2643  2021-03-10               South West      3
## 2644  2021-03-11               South West      2
## 2645  2021-03-12               South West      1
## 2646  2021-03-13               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2021-03-14"

The completion date of the NHS Pathways data is Sunday 14 Mar 2021.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 15 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 15 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -19.208  -16.158   -4.946    6.359   32.735  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 5.231e+00  6.429e-02  81.363   <2e-16 ***
## note_lag    1.131e-05  1.230e-06   9.188   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 217.7271)
## 
##     Null deviance: 81623  on 324  degrees of freedom
## Residual deviance: 68038  on 323  degrees of freedom
##   (15 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 5

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  186.909689    1.000011
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 164.414389 211.555321
## note_lag      1.000009   1.000014

Rsq(lag_mod)
## [1] 0.166436

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                             sysname 
##                                                                                            "Darwin" 
##                                                                                             release 
##                                                                                            "19.6.0" 
##                                                                                             version 
## "Darwin Kernel Version 19.6.0: Tue Jan 12 22:13:05 PST 2021; root:xnu-6153.141.16~1/RELEASE_X86_64" 
##                                                                                            nodename 
##                                                                           "Mac-1615802812761.local" 
##                                                                                             machine 
##                                                                                            "x86_64" 
##                                                                                               login 
##                                                                                              "root" 
##                                                                                                user 
##                                                                                            "runner" 
##                                                                                      effective_user 
##                                                                                            "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.4                         
## year           2021                        
## month          02                          
## day            15                          
## svn rev        80002                       
## language       R                           
## version.string R version 4.0.4 (2021-02-15)
## nickname       Lost Library Book

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.4 (2021-02-15)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.5     ggpubr_0.4.0         lubridate_1.7.10    
##  [4] chngpt_2020.10-12    cyphr_1.1.0          DT_0.17             
##  [7] kableExtra_1.3.4     janitor_2.1.0        remotes_2.2.0       
## [10] projections_0.5.2    earlyR_0.0.5         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.3      rio_0.5.26          
## [16] reshape2_1.4.4       rvest_1.0.0          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.1        stringr_1.4.0       
## [22] dplyr_1.0.5          purrr_0.3.4          readr_1.4.0         
## [25] tidyr_1.1.3          tibble_3.1.0         ggplot2_3.3.3       
## [28] tidyverse_1.3.0      here_1.0.1           reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] minqa_1.2.4       colorspace_2.0-0  selectr_0.4-2     ggsignif_0.6.1   
##  [5] ellipsis_0.3.1    rprojroot_2.0.2   snakecase_0.11.0  fs_1.5.0         
##  [9] rstudioapi_0.13   farver_2.1.0      fansi_0.4.2       splines_4.0.4    
## [13] knitr_1.31        jsonlite_1.7.2    nloptr_1.2.2.2    broom_0.7.5      
## [17] dbplyr_2.1.0      compiler_4.0.4    httr_1.4.2        backports_1.2.1  
## [21] assertthat_0.2.1  Matrix_1.3-2      cli_2.3.1         htmltools_0.5.1.1
## [25] tools_4.0.4       gtable_0.3.0      glue_1.4.2        Rcpp_1.0.6       
## [29] carData_3.0-4     cellranger_1.1.0  vctrs_0.3.6       svglite_2.0.0    
## [33] nlme_3.1-152      matchmaker_0.1.1  crosstalk_1.1.1   xfun_0.22        
## [37] ps_1.6.0          openxlsx_4.2.3    lme4_1.1-26       lifecycle_1.0.0  
## [41] statmod_1.4.35    rstatix_0.7.0     MASS_7.3-53       scales_1.1.1     
## [45] hms_1.0.0         parallel_4.0.4    sodium_1.1        yaml_2.2.1       
## [49] curl_4.3          gridExtra_2.3     stringi_1.5.3     highr_0.8        
## [53] kyotil_2020.10-12 boot_1.3-26       zip_2.1.1         rlang_0.4.10     
## [57] pkgconfig_2.0.3   systemfonts_1.0.1 evaluate_0.14     lattice_0.20-41  
## [61] labeling_0.4.2    htmlwidgets_1.5.3 cowplot_1.1.1     tidyselect_1.1.0 
## [65] plyr_1.8.6        magrittr_2.0.1    R6_2.5.0          generics_0.1.0   
## [69] DBI_1.1.1         mgcv_1.8-33       pillar_1.5.1      haven_2.3.1      
## [73] foreign_0.8-81    withr_2.4.1       survival_3.2-7    abind_1.4-5      
## [77] modelr_0.1.8      crayon_1.4.1      car_3.0-10        utf8_1.2.1       
## [81] rmarkdown_2.7     viridis_0.5.1     grid_4.0.4        readxl_1.3.1     
## [85] data.table_1.14.0 reprex_1.0.0      digest_0.6.27     webshot_0.5.2    
## [89] munsell_0.5.0     viridisLite_0.3.0